xenharmonic (microtonal wiki)

A "superfourth" is an interval too wide to sound like a perfect fourth and too narrow to sound like a tritone. Margo Schulter, in her article Regions of the Interval Spectrum, proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in Just Intonation are 11/8 (about 551.3¢) and 15/11 (about 537¢), both undecimal (11-based) superfourths; and 48/35 (about 546.8¢) and 49/36 (about 533.7¢), both septimal (7-based) superfourths.

The inversion of a superfourth is a subfifth.

Of course, it should never be taken for granted that these categories are subjective and culturally influenced, and the borders are "fuzzy". Other description are possible and legitimate.

Examples

Below is a list of some intervals in the superfourth range, both just and tempered.

Interval	Cents Value	Prime Limit (if applicable)
6\88cET or 11\25edo	528.000	-
19/14	528.687	19
87/64	531.532	29
34/25	532.328	17
4\9edo	533.333	-
49/36	533.742	7
64/47	534.493	47
15/11	536.951	11
13\29edo	537.931	-
56/41	539.764	41
9\20edo	540.000	-
41/30	540.794	41
175/128	541.453	7
14\31edo	541.935	-
26/19	543.015	19
5\11edo	545.455	-
37/27	545.479	37
48/35	546.815	7
11\24edo	550.000	-
11/8	551.318	11
6\13edo	553.846	-
62/45	554.812	31
40/29	556.737	29
13\28edo	557.143	-
243/176	558.457	11
29/21	558.796	29
47/34	560.551	47
7\15edo	560.000	-